HELP! STATISTICS

Directions: Do any 8 of the 11 problems. Use the data below “movie data,”

This is due on May 22nd at 7 pm.

Directions for this assignment:

Please show all work, writing explanations of intermediate steps wherever appropriate. Clearly label all graphs, including the scale on the horizontal and vertical axes and the units of measure where appropriate.

You may use your notes, your textbook, any other resource book, a graphing calculator or computer software (subject to the statement above about showing intermediate steps) as resources. You may consult with other students in this class, but you cannot simply copy another student’s answer and submit it as your own. You may not seek help on these specific questions (or any questions with only minor modifications) from any person who is not in this class. Typing your name below indicates that you followed the rules in completing this assignment (please submit in this statement with your solutions):

Signed__________________________________________

Problems #1 – 6 refer to the data in the file “movie data,”

1. Organize the data for “Noms”(nominations) in an ungrouped frequency distribution. Show how to use the frequency distribution to find the mean, median, and standard deviation. Find the percent of observations within 1, 2 and 3 standard deviations of the mean for the “noms” data.

2. Make a grouped frequency distribution for “% of box office before nom” using 0.1 - 20 as the class limits of the first class. Draw a histogram and discuss its shape. Predict, from the shape of the histogram, whether the mean is greater than the median or vice-versa. Calculate the mean and the median. Was your prediction correct?

3. Make and interpret the meaning of a 95% confidence interval for the mean run time of all movies using the run time data for this sample of movies.

4. Conduct a hypothesis test to determine whether the mean box office for films released in December or November is higher than the mean box office for films released in other months using α = 0.025

5. Determine the correlation coefficient between production budget and the number of theatres and interpret its meaning. Plot a scatterplot.

6. Find the least squares linear regression equation for production budget and run time. Interpret the meaning of the slope and the y-intercept.

7. A search engine company claims that 25% of people who use its site click for more information about its advertisers’ products. Assuming that claim is true,

(a) what is the probability that at least one out of the next 8 people who use the site will click for more information?

(b) Estimate, using the normal distribution, the probability that at least 10 out of the next 80 people who use the site will click for more information.

(c) Write a few sentences describing why the answer to (b) is higher than the answer to part (a). Why would the answer be even higher if you estimated the probability that at least 1000 out of 8000 click for more info?

8. An accountant is studying the time it takes a company to make payments on accounts payable. The mean time it takes to pay off an invoice is 13.8 days with a standard deviation of 4.3 days, and the times are normally distributed.

(a) What is the probability that an account is paid off in less than 16 days?

(b) Find the 95th percentile for the payoff time- that is, a time for which 95% of the

accounts are paid off in less than that time.

(c) The company has just received 29 invoices. Find the probability that the mean payoff

time for these invoices is more than 16 days.

9. Suppose heights of U.S. adults are normally distributed with a mean of 66.3 and a standard deviation of 4.4 inches.

(a) Find the height such that 95% of the population is less than this height. (the 9